The Celsius to Fahrenheit formula: F=9/5C+32


Solve this formula for C. Check all answers that are true.

(4 points)
Responses

First step is to multiply by 9 on each side.
First step is to multiply by 9 on each side.

First step is to add 32 to both sides.
First step is to add 32 to both sides.

The next step from F - 32 = 9/5 C, could be to multiply both sides by 5
The next step from F - 32 = 9/5 C, could be to multiply both sides by 5

The next step from F - 32 = 9/5 C, could be to divide both sides by 5
The next step from F - 32 = 9/5 C, could be to divide both sides by 5

Solution: 5/9F - 32 = C
Solution: 5/9F - 32 = C

To solve this equation for C, you would have to distribute at some point.

1 answer

Given the Celsius to Fahrenheit formula:

\[ F = \frac{9}{5}C + 32 \]

Let's solve this equation for \( C \):

  1. Subtract 32 from both sides: \[ F - 32 = \frac{9}{5}C \]

  2. Multiply both sides by \( \frac{5}{9} \) (which is equivalent to dividing by \( \frac{9}{5} \)): \[ C = \frac{5}{9}(F - 32) \]

This expression can be written as: \[ C = \frac{5}{9}F - \frac{5}{9} \cdot 32 \] But it is not necessary to distribute 5/9 in the context of solving for \( C \).

Now we can check each statement regarding the steps taken:

  1. First step is to multiply by 9 on each side.

    • False: The first step is to subtract 32 from both sides, not to multiply.
  2. First step is to add 32 to both sides.

    • False: The first step is to subtract 32 from both sides.
  3. The next step from \( F - 32 = \frac{9}{5} C \), could be to multiply both sides by 5.

    • False: The correct operation is to multiply both sides by \( \frac{5}{9} \) to isolate \( C \).
  4. The next step from \( F - 32 = \frac{9}{5} C \), could be to divide both sides by 5.

    • False: The step here involves multiplying by \( \frac{5}{9} \), not dividing by 5.
  5. Solution: \( \frac{5}{9}F - 32 = C \)

    • False: The correct expression should be written as \( C = \frac{5}{9}(F - 32) \) instead, which clearly shows the relation.
  6. To solve this equation for C, you would have to distribute at some point.

    • False: While you can distribute after arriving at the expression \( C = \frac{5}{9}(F - 32) \), it's not necessary to solve for \( C \) in its isolated form. The most simplified isolated form of \( C \) can be kept as \( C = \frac{5}{9}(F - 32) \).

In summary, all of the provided statements are false.